To understand the role that pump pulses play in the measurement of specific viscosity it is instructive to first consider the single capillary viscometer as shown in FIG. 1. A pump 101 draws fluid from a reservoir 102 and passes it through a sensing capillary 103. A differential transducer 104 measures the pressure across the capillary. The measured pressure is proportional to the flow rate and the sample viscosity. If one first flows solvent through the capillary and measures the pressure P0, and subsequently injects a sample, the specific viscosity is simplyηsp=Ps/P0  (1)If the sample composition varies over in time, as is the case with the elution of a chromatographic separation, the specific viscosity as a function of time is simplyηsp(t)=Ps(t)/P0.
A problem arising from such a flowing system is that if the pump is not perfectly stable, pressure pulses appear identical to changes in the sample viscosity. Since the output of the conventional viscometer is directly proportional to the pressure, the sensitivity of such a device is limited by the quality of the pump used. High quality chromatography solvent delivery systems commonly provide solvent with pressure pulses less than 0.1%, so the ability to measure specific viscosity is limited to this level. However, high quality viscometers, such as the ViscoStar® (Wyatt Technology Corporation, Santa Barbara, Calif.) are able to routinely measures specific viscosity down to 1E-6, which is three orders of magnitude smaller, and therefore the improved sensitivity of measurements from high quality viscometers such as these is lost in the noise of the pump pulses from chromatography systems employing even the finest pumps available.
As an example of the output of a single capillary viscometer consider the chromatographic elution shown in FIG. 2. Two mg of Bovine Serium Albumen (BSA) was injected on a protein column (Wyatt Technology, Santa Barbara, Calif.) at a flow rate of 0.6667 ml/min, and the solvent was phosphate buffered saline. The pump was an Agilent® 1100 series pump (Agilent Technologies, Santa Clara, Calif.). As the detector is positioned after the column, the pump pulses are further dampened. In line following the viscometer was a Optilab® rEX concentration detector (Wyatt Technology Corporation, Santa Barbara, Calif.) that measured the differential refractive index 201 of the resulting elution. In spite of the fact that a high quality chromatography pump was used, the pump pulses limit the performance as is evident in the viscometry data 202.
One way to ameliorate the problem of pump pulses masquerading as sample peaks is to use a capillary bridge viscometer such as that described by Haney in 1982 in U.S. Pat. No. 4,463,598. The capillary bridge viscometer is a fluid analog of the classical Wheatstone bridge electrical circuit in which four capillaries are connected in a bridge formation along with a large fluid reservoir in one of the lower bridge arms. The delay volume insures that the bridge will go out of balance when a sample is introduced to the bridge. Data can be taken until the sample emerges from the delay column at which time one must wait for the column to refill with solvent before another sample may be injected. The out-of balance pressure is measured by a differential pressure transducer (DP), and the pressure from top to bottom of the bridge is measured by a separate transducer (IP). These two signals can be combined to determine the specific viscosity, ηsp, through the relation
                              η          sp                =                                                            η                s                                            η                0                                      -            1                    =                                    4              ⁢                                                          ⁢              DP                                      IP              -                              2                ⁢                                                                  ⁢                DP                                                                        (        2        )            where ηs is the sample viscosity, and η0 is the solvent viscosity. If the pump that drives the fluid through the system is not perfectly stable the system pressure, as well as the flow rate, fluctuate periodically. The assumption is that both sides of the DP transducer experience the same pressure pulses so that the differential nature of the transducers cancels out the pressure pulses. When the bridge is filled with pure solvent the DP signal should always equal zero.
By contrast, the IP transducer experiences no such cancellation. This is clear if one considers the Thévenin equivalent circuit associated with the bridge, as shown in FIG. 3. The bridge appears to be two series capillaries of impedance R (the left side of the bridge) in parallel with two series capillaries of impedance R (the right side of the bridge). The resulting circuit as seen by the IP transducer is simply a single capillary of impedance R. Therefore the IP transducer acts, for all intents and purposes, as a single capillary viscometer, with all of the problems of pump pulse pickup.
FIG. 4 presents data from a single capillary viscometer taken from a chromatographic elution of Bovine Serum Albumin (BSA) fractionated by a size exclusion column. The DP signal 401 is nearly free of pump pulses, whereas the IP signal 402 is not. The primary problem with the strong pump pulse reduction seen in FIG. 4 is that much of the benefit seen is not due to bridge cancellation. Instead pump pulses are suppressed because the DP sensor has a very slow time constant (˜9 seconds) and is acting as a low pass filter, thus not offering the advantage of high resolution one expects from a high quality viscometer.
The time constant of the sensors in the system can be determined by performing a simple experiment. FIG. 5 shows the response of the instrument to a rapid change in the applied flow rate from 0.5 ml/min to 1.0 ml/min. The IP signal 501 jumps from 5.5 psi to 11 psi as expected, and equilibrates to the new valve with a time constant around 0.5 seconds. The DP signal 502, in contrast, has an initial perturbation and equilibrates to a new equilibrium value with a 9 second time constant.
The low pass filtering that occurs from slow sensors works well to eliminate pulses when the pressure oscillations are much faster than the characteristic time scale of the underlying peak. In the example shown in FIG. 6, a standard ViscoStar® II viscometer (Wyatt Technology Corporation, Santa Barbara, Calif.) equipped with a Validyne pressure transducer (Validyne Engineering, Northridge, Calif.) was used to measure a sample peak. The peak consisted of 100 μl of 2 mg/ml BSA injected directly into the viscometer. The flow rate was 0.6667 ml/min. The viscometer was configured with only the short delay column to reduce the sample runs to only a few minutes. The Validyne transducer has a time constant of around 9 seconds, and the pump pulses at this flow rate have a fundamental period of 1.85 seconds (frequency=0.54 Hz). The peak width is 30 seconds. Since the pump pulses are much faster than the sensor time constant it is undeniably effective at suppressing them.
Consider the difference in performance between using a slow sensor and a fast one. FIG. 7 shows data taken with the same system configured with DP86 transducers (Measurement Specialties, Fremont, Calif.). Measurements showed that these transducers have a time constant around 0.2 seconds in this system. As seen in FIG. 7, the pump pulses are very obvious. Therefore it can be deduced that the pulses were always present, but the Validyne transducers, because of their slow response, were suppressing them.
The problem with suppressing pump pulses by using a slow sensor or a low pass filter is that the sample peak is also distorted. To make this clear the data in FIG. 7 subjected to a 9 second moving average filter to simulate the effect of a slow transducer. The results are shown in FIG. 8. Contrast the raw signal 801 with the filtered data 802. As expected, the filtered data is nearly free from pump pulses, but the underlying peak is distorted. This will negatively impact the accuracy of any results derived from the distorted data. Moreover, recent trends in the chromatography industry have been working towards the improvement of peak resolution and shorten run times. New generations of uPLC chromatography systems have peaks that are only 10 seconds wide (or less). As peaks become narrower, the measured signals become progressively more distorted. Clearly using slow sensors to suppress pump pulses does not scale well.